The normal line to the circle x² + y² = 25 at (2, 3) is?
- 3x + 2y = 0
- 3x - 2y = 0
- 3x + 2y + 1 = 2
- None of these
Explanation
Normal Line to a Circle
Given circle equation: x² + y² = 25
This is a circle with center (0,0) and radius 5.
Given point: (2,3)
The normal line at a point on the circle is the line passing through the center and the point.
The slope of the line joining (0,0) and (2,3) is 3/2.
The equation of the line passing through (0,0) and (2,3) can be found using point-slope form y = mx, where m is the slope.
So, y = (3/2)x
Multiplying both sides by 2 to get rid of the fraction: 2y = 3x
Rearranging: 3x - 2y = 0
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